If it is potentially damaging to national security, then it is going to be classified at some level. And yes, the President always has the power to waive it.
If Trump had declassified everything like you suggested odds are good he would have declassified potentially damaging things - just so he could take them home.
In this case it doesn't really matter because according to the warrant they're using the Espionage Act which doesn't rely on the documents being classified - only potentially damaging to national security.